Quantum algorithms promise computational speed-ups over their classical counterparts. Quantum phase estimation is a technique used in quantum algorithms, including algorithms for quantum chemistry (see, A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Science 309, 1704 (2005), and B. P. Lanyon, J. D. Whitfield, G. G. Gillet, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, Nature Chemistry 2, 106, 2008, arXiv:0905.0887), and quantum field theory (see, S. P. Jordan, K. S. M. Lee, and J. Preskill, “Quantum computation of scattering in scalar quantum field theories,” (2011), arXiv: 1112.4833), Shor's algorithm for prime factorization (see, P. Shor, SIAM Journal of Computing 26, 1484 (1997)), and algorithms for quantum sampling (see, M. Ozols, M. Roetteler, and J. Roland, in 3rd Innovations in Theoretical Computer Science Conference (ITCS), (ACM, 2012) pp. 290{308, arXiv:1103.2774, and also K. Temme, T. Osborne, K. Vollbrecht, D. Poulin, and F. Verstraete, Nature 471 (2011), 10.1038/nature09770, arXiv:0911.3635). Quantum phase estimation can also be used to find eigenvalues of a unitary matrix efficiently.